In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant regardless of external forces exerted on it. Engineers use rigid bodies to represent mechanical objects or parts (e.g., automobiles, engine blocks, etc) in an engineering analysis or simulation (e.g., finite element analysis). Sometimes, a mechanical part that is relatively rigid compared to the neighboring parts can also be modeled as rigid body. In many instance, simulating dynamic behaviors of a rigid body requires that three-dimensional motions be specified at a particular location on the rigid body. Physically, the motions of a mechanical object are measured by an instrument called accelerometer, which is an electromechanical device that is used for measuring acceleration forces. These forces may be static, like the constant force of gravity pulling at your feet, or they could be dynamic—caused by moving or vibrating the accelerometer.
In order to measure the acceleration of a relatively large mechanical object such as automobile, more than one accelerometer must be placed in different locations independently. The recorded accelerations can then be converted to a set of three-dimensional motions at any point of interest on the mechanical object. However, converting such measured data is not straight forward and has a number of problems including, but not necessarily limited to, 1) reducing redundant data, 2) minimizing measurement error, and 3) producing consistent determination.
Therefore, it would be desirable to have a new improved method to determine rigid body motion using data collected from independent accelerometers directly.